I disassembled the whole system, because of the beeps and the many resets, having an intense cleaning in mind.
When I took the mainboard out of the case, I noticed that there was thermal grease spotwise worn off both the CPU and the GPU. Also I noticed one missing heatpad and three heatpads that shrinked to about 65% in area.
So far, thats what Ive done:
Changed the Bios Battery.
Cleaned everything, especially CPU and GPU Surface.
Put new Thermal grease of most recent quality (5-10 W/mK) onto the CPU and GPU.
Put new Silicone Heatpads onto the ICs where I found the old wornout pads, especially the chipset-IC is now completely covered by a pad.
Reassembled and tested.
I experienced one more crash beeping - I guess its about the bios battery change - and I had to reactivate my system.
Since then everything is running fine again now.
Seems to have been a thermal issue because of the wornout pads and the broken thermal grease.